| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Condition for further/no further collision |
| Difficulty | Standard +0.8 This M2 mechanics question requires multiple collision analysis with restitution coefficients, involving systematic application of conservation of momentum and Newton's law of restitution across two collisions, then proving inequality conditions for collision occurrence. While methodical, it demands careful algebraic manipulation and physical reasoning about relative velocities across successive events, placing it moderately above average difficulty. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
\begin{enumerate}
\item Three identical particles $P , Q$ and $R$, each of mass $m$, lie in a straight line on a smooth horizontal plane with $Q$ between $P$ and $R$. Particles $P$ and $Q$ are projected directly towards each other with speeds $4 u$ and $2 u$ respectively, and at the same time particle $R$ is projected along the line away from $Q$ with speed $3 u$. The coefficient of restitution between each pair of particles is $e$. After the collision between $P$ and $Q$ there is a collision between $Q$ and $R$.\\
(a) Show that $e > \frac { 2 } { 3 }$
\end{enumerate}
It is given that $e = \frac { 3 } { 4 }$\\
(b) Show that there will not be a further collision between $P$ and $Q$.\\
\hfill \mbox{\textit{Edexcel M2 2015 Q8 [13]}}